Modal Frame Correspondence Generalized
Johan van Benthem
Abstract:
We show how first-order modal frame correspondence methods can be
generalized to deal with axioms like Löb's, provided we compute
minimal substitutions in a fixed-point extension of first-order
logic. Then we restore the harmony by also considering frame
correspondence for modal fixed-point languages like PDL or the
MU-calculus. We show how the latter leads to elegant and quite
workable proof systems, and hence to versions of modal logic and
provability logic that may be at least as natural in many ways. This
paper will appear in a special issue of "Studia Logica" devoted to the
memory of Wim Blok.
Keywords: modal logic; frame correspondence; ; fixed-point logic; substitution algorithm; ; minimal predicates; provability logic; ; Löb's axiom